Franke & Degen (2016), Reasoning in reference games, PLoS one 11(5)
(c.f., Camerer 2006, Franke 2011, Jaeger 2014)
\[\underbrace{\frac{P(M_1 \mid D)}{P(M_2 \mid D)}}_{\text{posterior odds}} = \underbrace{\frac{P(D \mid M_1)}{P(D \mid M_2)}}_{\text{Bayes factor}} \ \underbrace{\frac{P(M_1)}{P(M_2)}}_{\text{prior odds}}\]
\[ P(D \mid M_i) = \int P(\theta \mid M_i) \ P(D \mid \theta, M_i) \ \text{d}\theta \] - Bayes factors thereby implicitly penalize models with wide-spread a priori predictions and favor models which make precise predictions (if these are borne out by the data) - as models with
we use the Savage-Dickey method to approximate Bayes factors: